http://arxiv.org/abs/1912.06584
The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime—that is, where one mass is significantly smaller than the other—in the full context of our contemporary theory of gravity, general relativity. We divide this work into two broad parts: the first provides an overview of the theory of general relativity along with the basic mathematical methods underlying it, focusing on its canonical formulation and perturbation techniques; the second presents our novel work in these areas, focusing on the problems of entropy, motion and the self-force in general relativity. We begin here with a study of entropy theorems in classical Hamiltonian systems, and in particular, the issue of the second law of thermodynamics in classical mechanics and general relativity. Then, we develop a general approach based on conservation laws for calculating the correction to the motion of a sufficiently small object due to gravitational perturbations in general relativity. When the perturbations are attributed to the small object itself, this effect is known as the gravitational self-force. It is what drives the orbital evolution of extreme-mass-ratio inspirals: compact binary systems where one mass is much smaller than—thus effectively orbiting and eventually spiralling into—the other, expected to be among the main sources for the future space-based gravitational wave detector LISA. Finally, we present some work on the numerical computation of the scalar self-force using an approach called the Particle-without-Particle method, as well as the generalization of this method to general partial differential equations and applications to other areas of applied mathematics.
M. Oltean
Mon, 16 Dec 19
42/62
Comments: PhD thesis, Autonomous University of Barcelona and University of Orl\’eans, 2019 (302 pages, 39 figures)